Colours from imported MP4 screencast video look dull in Blender
Nevermind, it was my mistake: I had changed the default colour management in the Blender startup file to the new "Filmic" rendering and apparently, that's not what you'd want to use in this case... After changing it back to "Default" everything looks as intended.

I guess a new question could be: How would I handle this in a scenario where I actually want to use Filmic, e.g. if I were to set up a 3D scene where this video was shown on a TV screen? How would I have to adjust the settings for the video to display with its original colours?